physics of and with electron beam ion traps · 2018. 11. 14. · electron-ion interactions number...
TRANSCRIPT
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Physics of and with Electron Beam Ion Traps and Sources
EBIS/TFred Currell
Centre for Plasma PhysicsQueen’s University, Belfast
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Overview
• Trapping the ions• Electron ion interactions to build the
charge balance• Energetics of the ions in the trap• Controlling the EBIST to study physics of
electron - ioninteractions– Electron impact ionisation– Dielectronic Recombination
• Summary2
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Everything should be made as simple as possible, but not one bit simpler.
Albert Einstein, (attributed)
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Laplace’s equation
Poisson’s equation
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Why are Highly Charged Ions Interesting?
H He+ U91
+
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Binding energy
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Orbital velocity of the 1s electron
Relativistic
0 20 40 60 80 100Z0
5.0�107
1.0�108
1.5�108
2.0�108
2.5�108
3.0�108
3.5�108v�m�s�
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Quantum Electro Dynamics (QED)
In QED, the electromagnetic field is quantized.QED coupling constant is ve/c
QED calculations look like series (Zα)n
Quantum Electro Dynamical
0 20 40 60 80 100Z0.0
0.2
0.4
0.6
0.8
1.0ZΑn
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Orbital radius of the 1s electron
Nuclear Size Affected
20 40 60 80Z
1.�10�9
2.�10�9
3.�10�9
4.�10�9
5.�10�9
r�m�
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viii THE PHYSICS OF MULTIPLY AND HIGHLY CHARGED IONS
Land of knowledge
Sea of ignorance
Ionic Charge
Atomic Number
092
92
1 Neutral
matter
SSJ
Figure I.1. Parametersation of the world of atomic physics
number) and ionic charge (the difference between the number of electrons and
protons). The claim at the beginning of the preface is that most of chemistry and
a large portion of atomic physics is concerned with 276 distinct species. These
276 species are contained in the thin sliver to the left hand side of this figure
labelled ‘neutral matter’ and two equally thin slivers either side corresponding
to singly charged positive and negative ions. The world of multiply and highly
charged ions is the remainder of this figure. When considering the overlap
between atomic and nuclear physics (for example, hyperfine interactions) one
has to introduce an additional dimension to account for isotope effects related
to variation in the nuclear structure. We will not consider this dimension here.
The figure above is based on a somewhat artistic reproduction of a figure
which has appeared elsewhere in several guises and a very loose interpretation
of what constitutes sufficient knowledge (i.e. the array of transitions elec-
trons bound in the system can undergo has been identified). A less artistic
version of this figure can be found in "On The Structure and Spectra of Mul-
tiply Charged Ions" by I. Martinson and I. Kink, in Trapping Highly Charged
Ions: Fundamentals and Applications, ed. J. Gillaspy, Nova Scientifc (2001).
Notwithstanding the looseness of the interpretation some trends are readily ap-
parent. Most of our knowledge lies to the left hand side. Not surprisingly, these
multiply charged ions are relatively easy to produce. Consequently they are
the most amenable to experimental study. For the more highly charged ions,
Astrophysics
Fusion, Xe, Mo, W ...
QED tests, high Z , few e
Nuclear effects
World of Atomic Physics
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Electron Beam Ion Trap (EBIT)
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The Electron Beam Ion Trap
V(z
)
ZB
(z)
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EnergyDynamics
Ion SpatialDistributions
Charge ChangingReactions
ElectronBeam
tem
pera
ture
det
erm
ine s
esca
pe ra
te
flow
of e
nerg
y as i
ons
chan
ge ch
arge
sta
te
overlap factors a nd wo rk
done expand ing ion cl oud
temp erature determ
ines
cloud size
overlap factors scaleelectron-ion interactions
number of ions normalisesdistributions and effects ion space-charge compensation
ikT
ikT
iN
ief ,
jif ,
ief ,
See F Currell + G Fussmann “Physics of Electron Beam Ion Traps and Sources”, IEEE Trans. Plas. Sci. 33 1763-1777 (2005) + refs therein
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Typical Time Scales•Radial motion of the ions 10nsec
•Axial motion of the ions 100nsec
•Ion-ion collisions 0.1 - 1msec
•Cross-field diffusion 1 - 10msec
•Charge changing 10msec - 10sec
•Axial escape 100msec - hours
EnergyDynamics
Ion SpatialDistributions
Charge ChangingReactions
ElectronBeam
tem
pera
ture
det
erm
ine s
esca
pe ra
te
flow
of e
nerg
y as i
ons
chan
ge ch
arge
sta
te
overlap factors a nd wo rk
done expand ing ion cl oud
temp erature determ
ines
cloud size
overlap factors scaleelectron-ion interactions
number of ions normalisesdistributions and effects ion space-charge compensation
ikT
ikT
iN
ief ,
jif ,
ief ,
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EnergyDynamics
Ion SpatialDistributions
Charge ChangingReactions
ElectronBeam
tem
pera
ture
det
erm
ine s
esca
pe ra
te
flow
of e
nerg
y as i
ons
chan
ge ch
arge
sta
te
overlap factors a nd wo rk
done expand ing ion cl oud
temp erature determ
ines
cloud size
overlap factors scaleelectron-ion interactions
number of ions normalisesdistributions and effects ion space-charge compensation
ikT
ikT
iN
ief ,
jif ,
ief ,
‘state’ variablesaxial densitytemperature
index i runs over all charge states of all species in the trap.This is not a unique choice but it provides a computationally convenient description
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EnergyDynamics
Ion SpatialDistributions
Charge ChangingReactions
ElectronBeam
tem
pera
ture
det
erm
ine s
esca
pe ra
te
flow
of e
nerg
y as i
ons
chan
ge ch
arge
sta
te
overlap factors a nd wo rk
done expand ing ion cl oud
temp erature determ
ines
cloud size
overlap factors scaleelectron-ion interactions
number of ions normalisesdistributions and effects ion space-charge compensation
ikT
ikT
iN
ief ,
jif ,
ief ,
![Page 18: Physics of and with Electron Beam Ion Traps · 2018. 11. 14. · electron-ion interactions number of ions normalises distributions and effects ion space-charge compensation kT i kT](https://reader033.vdocuments.us/reader033/viewer/2022053106/6070434983804b74df576013/html5/thumbnails/18.jpg)
EnergyDynamics
Ion SpatialDistributions
Charge ChangingReactions
ElectronBeam
tem
pera
ture
det
erm
ine s
esca
pe ra
te
flow
of e
nerg
y as i
ons
chan
ge ch
arge
sta
te
overlap factors a nd wo rk
done expand ing ion cl oud
temp erature determ
ines
cloud size
overlap factors scaleelectron-ion interactions
number of ions normalisesdistributions and effects ion space-charge compensation
ikT
ikT
iN
ief ,
jif ,
ief ,
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EnergyDynamics
Ion SpatialDistributions
Charge ChangingReactions
ElectronBeam
tem
pera
ture
det
erm
ine s
esca
pe ra
te
flow
of e
nerg
y as i
ons
chan
ge ch
arge
sta
te
overlap factors a nd wo rk
done expand ing ion cl oud
temp erature determ
ines
cloud size
overlap factors scaleelectron-ion interactions
number of ions normalisesdistributions and effects ion space-charge compensation
ikT
ikT
iN
ief ,
jif ,
ief ,
![Page 20: Physics of and with Electron Beam Ion Traps · 2018. 11. 14. · electron-ion interactions number of ions normalises distributions and effects ion space-charge compensation kT i kT](https://reader033.vdocuments.us/reader033/viewer/2022053106/6070434983804b74df576013/html5/thumbnails/20.jpg)
EnergyDynamics
Ion SpatialDistributions
Charge ChangingReactions
ElectronBeam
tem
pera
ture
det
erm
ine s
esca
pe ra
te
flow
of e
nerg
y as i
ons
chan
ge ch
arge
sta
te
overlap factors a nd wo rk
done expand ing ion cl oud
temp erature determ
ines
cloud size
overlap factors scaleelectron-ion interactions
number of ions normalisesdistributions and effects ion space-charge compensation
ikT
ikT
iN
ief ,
jif ,
ief ,
![Page 21: Physics of and with Electron Beam Ion Traps · 2018. 11. 14. · electron-ion interactions number of ions normalises distributions and effects ion space-charge compensation kT i kT](https://reader033.vdocuments.us/reader033/viewer/2022053106/6070434983804b74df576013/html5/thumbnails/21.jpg)
EnergyDynamics
Ion SpatialDistributions
Charge ChangingReactions
ElectronBeam
tem
pera
ture
det
erm
ine s
esca
pe ra
te
flow
of e
nerg
y as i
ons
chan
ge ch
arge
sta
te
overlap factors a nd wo rk
done expand ing ion cl oud
temp erature determ
ines
cloud size
overlap factors scaleelectron-ion interactions
number of ions normalisesdistributions and effects ion space-charge compensation
ikT
ikT
iN
ief ,
jif ,
ief ,
![Page 22: Physics of and with Electron Beam Ion Traps · 2018. 11. 14. · electron-ion interactions number of ions normalises distributions and effects ion space-charge compensation kT i kT](https://reader033.vdocuments.us/reader033/viewer/2022053106/6070434983804b74df576013/html5/thumbnails/22.jpg)
EnergyDynamics
Ion SpatialDistributions
Charge ChangingReactions
ElectronBeam
tem
pera
ture
det
erm
ine s
esca
pe ra
te
flow
of e
nerg
y as i
ons
chan
ge ch
arge
sta
te
overlap factors a nd wo rk
done expand ing ion cl oud
temp erature determ
ines
cloud size
overlap factors scaleelectron-ion interactions
number of ions normalisesdistributions and effects ion space-charge compensation
ikT
ikT
iN
ief ,
jif ,
ief ,
![Page 23: Physics of and with Electron Beam Ion Traps · 2018. 11. 14. · electron-ion interactions number of ions normalises distributions and effects ion space-charge compensation kT i kT](https://reader033.vdocuments.us/reader033/viewer/2022053106/6070434983804b74df576013/html5/thumbnails/23.jpg)
The trapping mechanisms for the ions
• Treat electrostatic terms as separable in r and z– good approximation for EBITs, even better for
longer EBISes• Ignore effects of B-field
– OK for ion clouds as crossing B costs no energy
• Include effects of ion charge in a self-consistent way based on Poisson’s equation 23
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Trapping Potentials
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Exercise 1
Treating it non-relativistically, work out the charge per unit length in a (cylindrical) electron beam of current I and energy E
Do the same for a relativistic beam
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Some basic electrostatics from Hyperphysics
Gauss' Law, Integral FormThe area integral of the electric field over any closed surface is equal to the net charge enclosed in the surface divided by the permittivity of space. Gauss' law is a form of one of Maxwell's equations, the four fundamental equations for electricity and magnetism. Gauss' law permits the evaluation of the electric field in many practical situations by forming a symmetric Gaussian surface surrounding a charge distribution and evaluating the electric flux through that surface.
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Exercise 2 (from a QUB 1st year tutorial question)
Often fundamental physics investigations involve the interaction of charged particle beams (protons, electrons etc.). In this question you will calculate the electric field due to such a beam. i) Consider an infinitely long, cylindrical, uniform charged particle beam of radius R, with a charge per unit length of Q. What is the charge in a cylinder of unit length and radius r lying along the axis (consider both cases r < R and r > R)?Hint uniform means the charge density is the same everywhere inside the beam. ii) Identify the relevant symmetries and hence determine the direction of the electric field everywhere, due to the charge in the beam. iii) Apply Gauss’s law to work out an expression for the magnitude electrostatic field everywhere (remember two cases r < R and r > R).
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Exercise 3
Take the expressions from the last exercise and from them derive an expression for the potential due to the beam we considered in exercise 1. In doing this define your zero of potential at r=0
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Radial Trapping Potential
typically about 10 V
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Axial Trapping Potential• Treat as a square
well (reasonable approximation)
• Depth of the potential determined by applied voltages
• Needs a small correction for the space-charge of the electron beam This term comes from the requirement
that our radial potential matches the boundary condition at the drift tubes. In the exercises we set the potential on-axis to be zero.
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Magnetic effects• Clearly the magnetic field effects the motion of the ions. • However, when collisions are considered, the magnetic field
doesn’t affect the spatial (equilibrium) distribution of the ions– Moving across the lines of B costs no energy– A more sophisticated treatment requires solution of the
Vlassov equation – There is a class of experiments where the e-beam is
turned off -> like a penning trap (already discussed by Jose)
31
[see F. J. Currell “The physics of electron beam ions traps, section 5” in Trapping highly charged ions: fundamentals and applications, ed. John Gillaspy, Nova Science Publishers, ISBN 1-56072-725-X. (1999), G. Fussmann, C. Biedermann, and R. Radtke,“EBIT: An Electron Beam Source for the Production and Confinement of Highly Ionized Atoms” in: ”Advanced Technologies Based on Wave and Beam Generated Plasmas”, Eds. H. Schluter and A. Shivarova, Dordrecht: Kluwer Academic Publishers, 429 (1999)]
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Trap terms, a summary
32
RadialAxial
square well, applied voltages plus small correction
Magneticnegligible when ion cloud distributions are considered
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Trap terms, a summary
33
Axial
A real ‘static’ trap for allpositive charge states
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EnergyDynamics
Ion SpatialDistributions
Charge ChangingReactions
ElectronBeam
tem
pera
ture
det
erm
ine s
esca
pe ra
te
flow
of e
nerg
y as i
ons
chan
ge ch
arge
sta
te
overlap factors a nd wo rk
done expand ing ion cl oud
temp erature determ
ines
cloud size
overlap factors scaleelectron-ion interactions
number of ions normalisesdistributions and effects ion space-charge compensation
ikT
ikT
iN
ief ,
jif ,
ief ,
![Page 35: Physics of and with Electron Beam Ion Traps · 2018. 11. 14. · electron-ion interactions number of ions normalises distributions and effects ion space-charge compensation kT i kT](https://reader033.vdocuments.us/reader033/viewer/2022053106/6070434983804b74df576013/html5/thumbnails/35.jpg)
EnergyDynamics
Ion SpatialDistributions
Charge ChangingReactions
ElectronBeam
tem
pera
ture
det
erm
ine s
esca
pe ra
te
flow
of e
nerg
y as i
ons
chan
ge ch
arge
sta
te
overlap factors a nd wo rk
done expand ing ion cl oud
temp erature determ
ines
cloud size
overlap factors scaleelectron-ion interactions
number of ions normalisesdistributions and effects ion space-charge compensation
ikT
ikT
iN
ief ,
jif ,
ief ,
![Page 36: Physics of and with Electron Beam Ion Traps · 2018. 11. 14. · electron-ion interactions number of ions normalises distributions and effects ion space-charge compensation kT i kT](https://reader033.vdocuments.us/reader033/viewer/2022053106/6070434983804b74df576013/html5/thumbnails/36.jpg)
Typical Time Scales•Radial motion of the ions 10nsec
•Axial motion of the ions 100nsec
•Ion-ion collisions 0.1 - 1msec
•Cross-field diffusion 1 - 10msec
•Charge changing 10msec - 10sec
•Axial escape 100msec - hours
Suggests that maybe each charge state should have its own temperature but that it is meaningful to ascribe a single temperature for all degrees of freedom for a given charge state
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Density Distribution
re
Using the Vlasov equation it is possible to show that due to the effect of ion-ion collisions, the magnetic field has no effect on the ion density distribution at equilibrium. It is determined by the electrostatic potential alone.
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Some integrals over the spatial distribution
38
No. of ions in the trap, of species i
No. of ions in the electron beam, of species i
The ratio of the two is called the overlap factor. It acts to scale electron - ion interactions
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Poisson’s equation for radial spatial distributions
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figure from the Lu paper
40
X. Lu and F.J.Currelll PHYSICAL REVIEW SPECIAL TOPICS - ACCELERATORS AND BEAMS 12, 014401 (2009)
Electron beam: energy, 2.65 keV; radius, 35 um; current 68 mA. The positive charged ions here used were Si ;axial density of 2.5 E+9/cm ; the temperature is 81 eV.
14+
3
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How important is the ion space charge?
• Depends on the machine set up. • Compensation for the charge of the
electron beam can range from negligible to close to 100%
• small compensation: shallow axial trap, axial ion escape dominates
• near 100%: deep axial trap, radial escape dominates
41
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EnergyDynamics
Ion SpatialDistributions
Charge ChangingReactions
ElectronBeam
tem
pera
ture
det
erm
ine s
esca
pe ra
te
flow
of e
nerg
y as i
ons
chan
ge ch
arge
sta
te
overlap factors a nd wo rk
done expand ing ion cl oud
temp erature determ
ines
cloud size
overlap factors scaleelectron-ion interactions
number of ions normalisesdistributions and effects ion space-charge compensation
ikT
ikT
iN
ief ,
jif ,
ief ,
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EnergyDynamics
Ion SpatialDistributions
Charge ChangingReactions
ElectronBeam
tem
pera
ture
det
erm
ine s
esca
pe ra
te
flow
of e
nerg
y as i
ons
chan
ge ch
arge
sta
te
overlap factors a nd wo rk
done expand ing ion cl oud
temp erature determ
ines
cloud size
overlap factors scaleelectron-ion interactions
number of ions normalisesdistributions and effects ion space-charge compensation
ikT
ikT
iN
ief ,
jif ,
ief ,
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Ion Creation + Trapping•Use a high current, high energy electron beam to
• stepwise ionize neutrals/low charged ions • provide radial trapping
•Use a series of drift tubes to provide axial trapping
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Overview
• In principle many charge states can be present in both the ground state and excited states
• ionisation moves ions up the charge staircase
• radiative recombination and charge exchange move ions down the charge staircase
• escape allows ions to jump right off• system is fed by source neutral or
lowly charged ions
45
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Electrons in a strong fieldA simple picture
Potential due to the nucleus
Kinetic energy of electron
Momentum of electron
Free electron
Bound electronn=1
n=2
n=3
n=4
Ee
Eb
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Bound MotionLike planets round the sun
n=1
n=2
n=3
n=4
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Free MotionRutherford scattering
n=1
n=2
n=3
n=4
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Some Electromagnetic effects
Classically, an accelerated charged particle emits electromagnetic waves.
Quantum mechanically, this results in transitions accompanied by emission of photons.
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Transitions between bound states
n=1
n=2
n=3
n=4
hν
Due to high charge multipole contributions are significant
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Radiative Recombination
n=1
n=2
n=3
n=4
Ee
Eb
hν
N.B. ion charge reduces by one
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Electron Impact Ionisation
n=1
n=2
n=3n=4
Ee
N.B. ion charge increases by one
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Charge Exchange
N.B. ion charge reduces by one, or possibly more (multiple electron transfer)
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Excited states
• Because of the high charge states we are concerned with, lots of forbidden transitions have a high transition rate
• As a result there are almost no metastable states in highly charged ions– there is a rare exception in Be-like ions
• Hence we can consider all of the ions to be in their ground electronic state
• They might be in excited hyperfine states but that doesnʼt affect the ionisation dynamics
54
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Overview• We can model the system by
considering the populations of each charge state
• Can consider ions as being in the ground electronic state
• Ions are not always in the electron beam
• Take this into account using ‘overlap factors’
55
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Coupled set of rate equations
56
or diagrammatically like this (includes multiple charge exchange)
ionisation
radiativerecombination
chargeexchange
escape
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EnergyDynamics
Ion SpatialDistributions
Charge ChangingReactions
ElectronBeam
tem
pera
ture
det
erm
ine s
esca
pe ra
te
flow
of e
nerg
y as i
ons
chan
ge ch
arge
sta
te
overlap factors a nd wo rk
done expand ing ion cl oud
temp erature determ
ines
cloud size
overlap factors scaleelectron-ion interactions
number of ions normalisesdistributions and effects ion space-charge compensation
ikT
ikT
iN
ief ,
jif ,
ief ,
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EnergyDynamics
Ion SpatialDistributions
Charge ChangingReactions
ElectronBeam
tem
pera
ture
det
erm
ine s
esca
pe ra
te
flow
of e
nerg
y as i
ons
chan
ge ch
arge
sta
te
overlap factors a nd wo rk
done expand ing ion cl oud
temp erature determ
ines
cloud size
overlap factors scaleelectron-ion interactions
number of ions normalisesdistributions and effects ion space-charge compensation
ikT
ikT
iN
ief ,
jif ,
ief ,
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Energy mechanisms• Electron-ion collisions
– Electron beam heating• Ion-ion collisions
– Sharing of energy among the ions
– Cross-field diffusion into spatial equilibrium distribution
• Axial escape– Preferential loss of low-
charge/ high-energy ions
– Depletes energy faster than population
p pzr
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Electron beam heating• Mostly due to many long range collisions
– Well known in plasma physics (e.g. Spitzer)• For an ion inside the electron beam, the
heating rate is Coulomb logarithm
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Ion-ion collisions• Equipartition time for ions of species i interacting
with species j
For similar charge states q-4
This is strongest for highly charged ions
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62
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Axial escape• High energy tails of the velocity
distribution escape– Axial component so 1-D
• They are replenished by velocity diffusion caused by collisions
Smaller but cooler
Initial axial velocity
distribution
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Ion measurement system
Acceleration Lens
DischargeIon Source (MEVVA)
Ionsfrom the EBIT
Analysing Magnet
Secondary Electron Multiplier(movable)
ElectrostaticBender
QuadrupoleLens
Deceleration Lens
Einzel Lens1
Einzel Lens2
Einzel Lens3
movableAperturefor Beam Profiling
Deflector 2
Deflector 1
Position SensitiveDetector(movable)
To Ion-Surface Experiment
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Raw Data
Warning, peak heights can not simply be interpreted as giving the charge balance dynamics without proper consideration of the iontemperatures as the extraction efficiency is temperature dependent
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Energy Dynamics•Compare escape rate to number trapped for two or more charge states
•Temperature dynamics
•Ion cloud distributions from Maxwellian
Surprise! kT(t=0) in not 0eV
Evidence for ionisation heating
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Density Distribution
re
Due to the effect of ion-ion collisions, the magnetic field has no effect on the ion density distribution. It is determined by the electrostatic potential alone.
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Reconstruction
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Work done expanding the ion cloud
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Work done expanding the ion cloud
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Work done expanding the ion cloudUndergrad thermo dynamics, C = no. degrees of freedom/2v
5 degrees of freedom1 associated with axial motion (free particle/gas atom)2 for each direction perpendicular to the electron beamc.f. ion in a crystal
3 degrees of freedom1 associated with each direction x,y,zfree particle/gas atom
2nd order phase transition of the electron beam + ion-cloud system
TypicalEBIT
TypicalEBIS
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Controllableparameter
Axial escape ratesBoth the number and the temperature decrease exponentially but the time constants are different
Av. Energy of trapped ions Av. Energy of
escaping ions
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Pulsed Evaporative Cooling (PEC)
• Gradually lower the trap barrier– Successively cooler ions, using evapouration
• Model the process including– Evaporative cooling equations– Electron beam heating equations– Electron-Ion overlap equations
Set of coupled differential equations which provide a description of PEC
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Simulation of PEC
Time through dump [msec]
Rel
ativ
e el
ectro
n-io
n in
tera
ctio
n ra
te
Ba46+, Ee=10keV, Ie=36mA
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DumpX-ray emission from Ba46+
Ee=10keV Ie=36mA
Trap refill
Measurement of PEC
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Cooling by PEC
Time through dump [msec]
Mea
n fr
ee p
ath
[m]
•Progressive lowering of the trap leads to
•cooling of the ions
• a collapse of the ion cloud
•increased electron-ion interaction rate
•decreased mean free path
Rel
ativ
e el
ectro
n-io
n in
tera
ctio
n ra
tekT
[eV
]
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Collapse of the Ion Cloud,‘phase-transition’-like behaviour
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EBIST programming• Quasi-equilibrium: set d(anything)/dt = 0
– electron impact ionisation, closed shell dielectronic recombination
• ‘Impulse’: fast changes, assume charge balance and temperatures are constant– open shell dielectronic recombination
• Normalise cross sections/rates using other (well known) rates
78
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EnergyDynamics
Ion SpatialDistributions
Charge ChangingReactions
ElectronBeam
tem
pera
ture
det
erm
ine s
esca
pe ra
te
flow
of e
nerg
y as i
ons
chan
ge ch
arge
sta
te
overlap factors a nd wo rk
done expand ing ion cl oud
temp erature determ
ines
cloud size
overlap factors scaleelectron-ion interactions
number of ions normalisesdistributions and effects ion space-charge compensation
ikT
ikT
iN
ief ,
jif ,
ief ,
Beam energy Ee
Beam current Ie
Substanceinjected (Z)
Trap depth Vt
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viii THE PHYSICS OF MULTIPLY AND HIGHLY CHARGED IONS
Land of knowledge
Sea of ignorance
Ionic Charge
Atomic Number
092
92
1 Neutral
matter
SSJ
Figure I.1. Parametersation of the world of atomic physics
number) and ionic charge (the difference between the number of electrons and
protons). The claim at the beginning of the preface is that most of chemistry and
a large portion of atomic physics is concerned with 276 distinct species. These
276 species are contained in the thin sliver to the left hand side of this figure
labelled ‘neutral matter’ and two equally thin slivers either side corresponding
to singly charged positive and negative ions. The world of multiply and highly
charged ions is the remainder of this figure. When considering the overlap
between atomic and nuclear physics (for example, hyperfine interactions) one
has to introduce an additional dimension to account for isotope effects related
to variation in the nuclear structure. We will not consider this dimension here.
The figure above is based on a somewhat artistic reproduction of a figure
which has appeared elsewhere in several guises and a very loose interpretation
of what constitutes sufficient knowledge (i.e. the array of transitions elec-
trons bound in the system can undergo has been identified). A less artistic
version of this figure can be found in "On The Structure and Spectra of Mul-
tiply Charged Ions" by I. Martinson and I. Kink, in Trapping Highly Charged
Ions: Fundamentals and Applications, ed. J. Gillaspy, Nova Scientifc (2001).
Notwithstanding the looseness of the interpretation some trends are readily ap-
parent. Most of our knowledge lies to the left hand side. Not surprisingly, these
multiply charged ions are relatively easy to produce. Consequently they are
the most amenable to experimental study. For the more highly charged ions,
Astrophysics
Fusion, Xe, Mo, W ...
QED tests, high Z , few e
Nuclear effects
World of Atomic Physics
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atom
ic n
umbe
r (Z
)
charge (Q)
Fundamentals and Applications
Astrophysics
Fusion, W, Mo, Xe, ...
QED tests, high Z , few
eNuclear effects
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H-like Electron Impact Ionisation
At equilibrium, H-like ionisation rate must equal the bare recombination rate,
provided we correct for charge exchange and assume effects of overlap factor and
escape cancel
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Electron Impact Ionisation Measurements
H-like Bare
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……
Mo data65keV 175mA electron beam
H-like
bare
1-2s
2-3s
18-19s
19-20s
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H-like
Bare
Intensity variation with timeMo 64.4keV 170mA
Equilibrium 7-16s
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Measurement of the Electron Impact Ionization Cross Section
measuretheory
theory
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The Electron Impact Ionization Cross Section of H-like Fe
IRON (Z=26)
B. O'Rourke B et al. J.Phys.B: 34 4002 (2001)
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The Electron Impact IonizationCross Section of H-like Mo
MOLYBDENUM (Z=42)
R. Marrs et al Phys Rev A 56 1338 (1997) H. Watanabe et al. J.Phys.B: 35 (2002)
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Comparison to theory
89
compilation of all measurements Z>20
Electron Energy/Ionisation Potential
O’Rourke,BE; Watanabe,H; Currell,FJ, “Electron Impact Ionisation of Hydrogen-like Ions” 2003, in “The Physics of Multiply and Highly Charged Ions: Vol.1 Sources, Applications and Fundamental Processes”, Ed. F.J. Currell Kluwer Academic Publishers, ISBN 1-4020-1565-8
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Bare Mo time evolutionMo+ and re varied
lines (from slowest to fastest onset) correspond to a beam radius of 66 , 62, 58, 52 and 48 µm respectively
B = 4.0T, Ee= 64.4 keV, Ie = 170mA, Vt = 50V
X.Lu and F Currell, Phys Rev special topics, accelerators and beams, 12 014401 (2009)
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H-like Mo time evolutionparameters as per previous
lines (from slowest to fastest onset) correspond to a beam radius of 66 , 62, 58, 52 and 48 µm respectively
B = 4.0T, Ee= 64.4 keV, Ie = 170mA, Vt = 50V
X.Lu and F Currell, Phys Rev special topics, accelerators and beams, 12 014401 (2009)
Discrepancy, calls some of the lower charge state ionisation cross-sections into question
![Page 92: Physics of and with Electron Beam Ion Traps · 2018. 11. 14. · electron-ion interactions number of ions normalises distributions and effects ion space-charge compensation kT i kT](https://reader033.vdocuments.us/reader033/viewer/2022053106/6070434983804b74df576013/html5/thumbnails/92.jpg)
Dielectronic recombination,He-like ions
Change beam energy quickly enough: ‘frozen’ charge balance. Correlate detected photons with
beam energy.
![Page 93: Physics of and with Electron Beam Ion Traps · 2018. 11. 14. · electron-ion interactions number of ions normalises distributions and effects ion space-charge compensation kT i kT](https://reader033.vdocuments.us/reader033/viewer/2022053106/6070434983804b74df576013/html5/thumbnails/93.jpg)
Dielectronic Recombination (DR)
• Resonant version of radiative recombination
• continuum electron trapped while another electron in the target is excited
• cross-section/rate can be orders of magnitude greater than for RR
• system stabilises by emission of one or more photons
• Photon(s) emitted, ion charge state decreased by one unit
![Page 94: Physics of and with Electron Beam Ion Traps · 2018. 11. 14. · electron-ion interactions number of ions normalises distributions and effects ion space-charge compensation kT i kT](https://reader033.vdocuments.us/reader033/viewer/2022053106/6070434983804b74df576013/html5/thumbnails/94.jpg)
Dielectronic Recombination (DR)
A q++ e- → [ ]A (q-1)+ ∗∗ → A(q-1)+ n ⋅ hν+
one or more photons: energy gives transition infodown-charged ion: gives total cross-section info
Resonance manifold denoted in inverse Auger notatione.g. KLM = 1s-1 2l 3l
![Page 95: Physics of and with Electron Beam Ion Traps · 2018. 11. 14. · electron-ion interactions number of ions normalises distributions and effects ion space-charge compensation kT i kT](https://reader033.vdocuments.us/reader033/viewer/2022053106/6070434983804b74df576013/html5/thumbnails/95.jpg)
Dielectronic Recombination
![Page 96: Physics of and with Electron Beam Ion Traps · 2018. 11. 14. · electron-ion interactions number of ions normalises distributions and effects ion space-charge compensation kT i kT](https://reader033.vdocuments.us/reader033/viewer/2022053106/6070434983804b74df576013/html5/thumbnails/96.jpg)
Experiment Layout
![Page 97: Physics of and with Electron Beam Ion Traps · 2018. 11. 14. · electron-ion interactions number of ions normalises distributions and effects ion space-charge compensation kT i kT](https://reader033.vdocuments.us/reader033/viewer/2022053106/6070434983804b74df576013/html5/thumbnails/97.jpg)
DR via the x-rays
KLL
KLMKLN
KMM KMN
RadiativeRecombination
![Page 98: Physics of and with Electron Beam Ion Traps · 2018. 11. 14. · electron-ion interactions number of ions normalises distributions and effects ion space-charge compensation kT i kT](https://reader033.vdocuments.us/reader033/viewer/2022053106/6070434983804b74df576013/html5/thumbnails/98.jpg)
He-like system
Scaling law: H. Watanabe et al.J. Phys. B 34 5095-5102 (2001)
Ti data point: B.O'Rourke et al.J.Phys B: 37 2343-2353 (2004)
€
S = 1m1Z 2 + m2Z−2
Fit to
![Page 99: Physics of and with Electron Beam Ion Traps · 2018. 11. 14. · electron-ion interactions number of ions normalises distributions and effects ion space-charge compensation kT i kT](https://reader033.vdocuments.us/reader033/viewer/2022053106/6070434983804b74df576013/html5/thumbnails/99.jpg)
hydrogen and helium like Ti
B. O'Rourke, et al Physical Review A, (2008), 77, 6, 062709
![Page 100: Physics of and with Electron Beam Ion Traps · 2018. 11. 14. · electron-ion interactions number of ions normalises distributions and effects ion space-charge compensation kT i kT](https://reader033.vdocuments.us/reader033/viewer/2022053106/6070434983804b74df576013/html5/thumbnails/100.jpg)
2l2
1s2l
1s2
KLL cascade
![Page 101: Physics of and with Electron Beam Ion Traps · 2018. 11. 14. · electron-ion interactions number of ions normalises distributions and effects ion space-charge compensation kT i kT](https://reader033.vdocuments.us/reader033/viewer/2022053106/6070434983804b74df576013/html5/thumbnails/101.jpg)
KLM cascade
![Page 102: Physics of and with Electron Beam Ion Traps · 2018. 11. 14. · electron-ion interactions number of ions normalises distributions and effects ion space-charge compensation kT i kT](https://reader033.vdocuments.us/reader033/viewer/2022053106/6070434983804b74df576013/html5/thumbnails/102.jpg)
2D Plot of Ti Data
![Page 103: Physics of and with Electron Beam Ion Traps · 2018. 11. 14. · electron-ion interactions number of ions normalises distributions and effects ion space-charge compensation kT i kT](https://reader033.vdocuments.us/reader033/viewer/2022053106/6070434983804b74df576013/html5/thumbnails/103.jpg)
Observe Li-like Ions at Early Times
Use Reject
![Page 104: Physics of and with Electron Beam Ion Traps · 2018. 11. 14. · electron-ion interactions number of ions normalises distributions and effects ion space-charge compensation kT i kT](https://reader033.vdocuments.us/reader033/viewer/2022053106/6070434983804b74df576013/html5/thumbnails/104.jpg)
Run charge dynamics modelonly Ti+ abundance fitted
X.Lu and F Currell, Phys Rev special topics, accelerators and beams, 12 014401 (2009)
![Page 105: Physics of and with Electron Beam Ion Traps · 2018. 11. 14. · electron-ion interactions number of ions normalises distributions and effects ion space-charge compensation kT i kT](https://reader033.vdocuments.us/reader033/viewer/2022053106/6070434983804b74df576013/html5/thumbnails/105.jpg)
Run charge dynamics modelonly Ti+ abundance fitted but DR now included
X.Lu and F Currell, Phys Rev special topics, accelerators and beams, 12 014401 (2009)
![Page 106: Physics of and with Electron Beam Ion Traps · 2018. 11. 14. · electron-ion interactions number of ions normalises distributions and effects ion space-charge compensation kT i kT](https://reader033.vdocuments.us/reader033/viewer/2022053106/6070434983804b74df576013/html5/thumbnails/106.jpg)
Dielectronic recombination of open L-shell ions
Look at energy dependence of ratios of neighbouring charge states (nq-1/nq), when we hit a DR resonance there
should be a maximum. Infer from extracted ions.
![Page 107: Physics of and with Electron Beam Ion Traps · 2018. 11. 14. · electron-ion interactions number of ions normalises distributions and effects ion space-charge compensation kT i kT](https://reader033.vdocuments.us/reader033/viewer/2022053106/6070434983804b74df576013/html5/thumbnails/107.jpg)
Ion measurement system
Acceleration Lens
DischargeIon Source (MEVVA)
Ionsfrom the EBIT
Analysing Magnet
Secondary Electron Multiplier(movable)
ElectrostaticBender
QuadrupoleLens
Deceleration Lens
Einzel Lens1
Einzel Lens2
Einzel Lens3
movableAperturefor Beam Profiling
Deflector 2
Deflector 1
Position SensitiveDetector(movable)
To Ion-Surface Experiment
![Page 108: Physics of and with Electron Beam Ion Traps · 2018. 11. 14. · electron-ion interactions number of ions normalises distributions and effects ion space-charge compensation kT i kT](https://reader033.vdocuments.us/reader033/viewer/2022053106/6070434983804b74df576013/html5/thumbnails/108.jpg)
Dielectronic recombination of open L-shell ions
Look at energy dependence of ratios of neighbouring charge states (nq-1/nq), when we hit a DR resonance there
should be a maximum. Infer from extracted ions.
![Page 109: Physics of and with Electron Beam Ion Traps · 2018. 11. 14. · electron-ion interactions number of ions normalises distributions and effects ion space-charge compensation kT i kT](https://reader033.vdocuments.us/reader033/viewer/2022053106/6070434983804b74df576013/html5/thumbnails/109.jpg)
Data analysis
![Page 110: Physics of and with Electron Beam Ion Traps · 2018. 11. 14. · electron-ion interactions number of ions normalises distributions and effects ion space-charge compensation kT i kT](https://reader033.vdocuments.us/reader033/viewer/2022053106/6070434983804b74df576013/html5/thumbnails/110.jpg)
Extracted ion energy dependence
![Page 111: Physics of and with Electron Beam Ion Traps · 2018. 11. 14. · electron-ion interactions number of ions normalises distributions and effects ion space-charge compensation kT i kT](https://reader033.vdocuments.us/reader033/viewer/2022053106/6070434983804b74df576013/html5/thumbnails/111.jpg)
Ratios of neighbouring charge states
![Page 112: Physics of and with Electron Beam Ion Traps · 2018. 11. 14. · electron-ion interactions number of ions normalises distributions and effects ion space-charge compensation kT i kT](https://reader033.vdocuments.us/reader033/viewer/2022053106/6070434983804b74df576013/html5/thumbnails/112.jpg)
Unknown, slowly varying with Ee
DR by change in ratio at eqm as a function of energy?
measured, rapidly varying with Ee
measured, rapidly varying with Ee
![Page 113: Physics of and with Electron Beam Ion Traps · 2018. 11. 14. · electron-ion interactions number of ions normalises distributions and effects ion space-charge compensation kT i kT](https://reader033.vdocuments.us/reader033/viewer/2022053106/6070434983804b74df576013/html5/thumbnails/113.jpg)
Corrected for charge exchange/escape
![Page 114: Physics of and with Electron Beam Ion Traps · 2018. 11. 14. · electron-ion interactions number of ions normalises distributions and effects ion space-charge compensation kT i kT](https://reader033.vdocuments.us/reader033/viewer/2022053106/6070434983804b74df576013/html5/thumbnails/114.jpg)
Add to He-like scaling data
Kavanagh,A.P et al, Phys. Rev. A, 81 022712 (2010)
€
S = 1m1Z 2 + m2Z−2
Fit to
![Page 115: Physics of and with Electron Beam Ion Traps · 2018. 11. 14. · electron-ion interactions number of ions normalises distributions and effects ion space-charge compensation kT i kT](https://reader033.vdocuments.us/reader033/viewer/2022053106/6070434983804b74df576013/html5/thumbnails/115.jpg)
and generate similar scaling laws for Li- and Be-like
€
S =1
m1Z2 + m2Z
−2Fit to
Kavanagh,A.P et al, Phys. Rev. A, 81 022712 (2010)
![Page 116: Physics of and with Electron Beam Ion Traps · 2018. 11. 14. · electron-ion interactions number of ions normalises distributions and effects ion space-charge compensation kT i kT](https://reader033.vdocuments.us/reader033/viewer/2022053106/6070434983804b74df576013/html5/thumbnails/116.jpg)
Li-like ions Z-dependence
N. Nakamura et alPRL 100, 7, 073203 (2008)
![Page 117: Physics of and with Electron Beam Ion Traps · 2018. 11. 14. · electron-ion interactions number of ions normalises distributions and effects ion space-charge compensation kT i kT](https://reader033.vdocuments.us/reader033/viewer/2022053106/6070434983804b74df576013/html5/thumbnails/117.jpg)
Z-dependence of GBI in Li-like ions
![Page 118: Physics of and with Electron Beam Ion Traps · 2018. 11. 14. · electron-ion interactions number of ions normalises distributions and effects ion space-charge compensation kT i kT](https://reader033.vdocuments.us/reader033/viewer/2022053106/6070434983804b74df576013/html5/thumbnails/118.jpg)
Be-like Bi line shape
N. Nakamura et al PRA 80, 014503 (2009)
![Page 119: Physics of and with Electron Beam Ion Traps · 2018. 11. 14. · electron-ion interactions number of ions normalises distributions and effects ion space-charge compensation kT i kT](https://reader033.vdocuments.us/reader033/viewer/2022053106/6070434983804b74df576013/html5/thumbnails/119.jpg)
Summary
EnergyDynamics
Ion SpatialDistributions
Charge ChangingReactions
ElectronBeam
tem
pera
ture
det
erm
ine s
esca
pe ra
te
flow
of e
nerg
y as i
ons
chan
ge ch
arge
sta
te
overlap factors a nd wo rk
done expand ing ion cl oud
temp erature determ
ines
cloud size
overlap factors scaleelectron-ion interactions
number of ions normalisesdistributions and effects ion space-charge compensation
ikT
ikT
iN
ief ,
jif ,
ief ,
We have looked at a model in terms ofelectron/ion interactions
(atomic physics, energetics etc.)
![Page 120: Physics of and with Electron Beam Ion Traps · 2018. 11. 14. · electron-ion interactions number of ions normalises distributions and effects ion space-charge compensation kT i kT](https://reader033.vdocuments.us/reader033/viewer/2022053106/6070434983804b74df576013/html5/thumbnails/120.jpg)
Summary
EnergyDynamics
Ion SpatialDistributions
Charge ChangingReactions
ElectronBeam
tem
pera
ture
det
erm
ine s
esca
pe ra
te
flow
of e
nerg
y as i
ons
chan
ge ch
arge
sta
te
overlap factors a nd wo rk
done expand ing ion cl oud
temp erature determ
ines
cloud size
overlap factors scaleelectron-ion interactions
number of ions normalisesdistributions and effects ion space-charge compensation
ikT
ikT
iN
ief ,
jif ,
ief ,
We have looked at a model in terms ofelectron/ion interactions
(atomic physics, energetics etc.)
![Page 121: Physics of and with Electron Beam Ion Traps · 2018. 11. 14. · electron-ion interactions number of ions normalises distributions and effects ion space-charge compensation kT i kT](https://reader033.vdocuments.us/reader033/viewer/2022053106/6070434983804b74df576013/html5/thumbnails/121.jpg)
Summary
EnergyDynamics
Ion SpatialDistributions
Charge ChangingReactions
ElectronBeam
tem
pera
ture
det
erm
ine s
esca
pe ra
te
flow
of e
nerg
y as i
ons
chan
ge ch
arge
sta
te
overlap factors a nd wo rk
done expand ing ion cl oud
temp erature determ
ines
cloud size
overlap factors scaleelectron-ion interactions
number of ions normalisesdistributions and effects ion space-charge compensation
ikT
ikT
iN
ief ,
jif ,
ief ,
We have looked at a model in terms ofelectron/ion interactions
(atomic physics, energetics etc.)
![Page 122: Physics of and with Electron Beam Ion Traps · 2018. 11. 14. · electron-ion interactions number of ions normalises distributions and effects ion space-charge compensation kT i kT](https://reader033.vdocuments.us/reader033/viewer/2022053106/6070434983804b74df576013/html5/thumbnails/122.jpg)
Summary
EnergyDynamics
Ion SpatialDistributions
Charge ChangingReactions
ElectronBeam
tem
pera
ture
det
erm
ine s
esca
pe ra
te
flow
of e
nerg
y as i
ons
chan
ge ch
arge
sta
te
overlap factors a nd wo rk
done expand ing ion cl oud
temp erature determ
ines
cloud size
overlap factors scaleelectron-ion interactions
number of ions normalisesdistributions and effects ion space-charge compensation
ikT
ikT
iN
ief ,
jif ,
ief ,
We have looked at a model in terms ofelectron/ion interactions
(atomic physics, energetics etc.)
![Page 123: Physics of and with Electron Beam Ion Traps · 2018. 11. 14. · electron-ion interactions number of ions normalises distributions and effects ion space-charge compensation kT i kT](https://reader033.vdocuments.us/reader033/viewer/2022053106/6070434983804b74df576013/html5/thumbnails/123.jpg)
Summary
EnergyDynamics
Ion SpatialDistributions
Charge ChangingReactions
ElectronBeam
tem
pera
ture
det
erm
ine s
esca
pe ra
te
flow
of e
nerg
y as i
ons
chan
ge ch
arge
sta
te
overlap factors a nd wo rk
done expand ing ion cl oud
temp erature determ
ines
cloud size
overlap factors scaleelectron-ion interactions
number of ions normalisesdistributions and effects ion space-charge compensation
ikT
ikT
iN
ief ,
jif ,
ief ,
This model can provide a reasonable account of the observed evolution of the
charge states in EBIST machines...
![Page 124: Physics of and with Electron Beam Ion Traps · 2018. 11. 14. · electron-ion interactions number of ions normalises distributions and effects ion space-charge compensation kT i kT](https://reader033.vdocuments.us/reader033/viewer/2022053106/6070434983804b74df576013/html5/thumbnails/124.jpg)
... and also provide a framework for the design of experiments
which probe these same electron-ion interactions
Electron impact ionisation Dielectronic Recombination
EnergyDynamics
Ion SpatialDistributions
Charge ChangingReactions
ElectronBeam
tem
pera
ture
det
erm
ine s
esca
pe ra
te
flow
of e
nerg
y as i
ons
chan
ge ch
arge
sta
te
overlap factors a nd wo rk
done expand ing ion cl oud
temp erature determ
ines
cloud size
overlap factors scaleelectron-ion interactions
number of ions normalisesdistributions and effects ion space-charge compensation
ikT
ikT
iN
ief ,
jif ,
ief ,
Summary
![Page 125: Physics of and with Electron Beam Ion Traps · 2018. 11. 14. · electron-ion interactions number of ions normalises distributions and effects ion space-charge compensation kT i kT](https://reader033.vdocuments.us/reader033/viewer/2022053106/6070434983804b74df576013/html5/thumbnails/125.jpg)
Thank you for your time and attention